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Maximal Operators Associated with Vector Polynomials of Lacunary Coefficients
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove the ${{L}^{P}}({{\mathbb{R}}^{d}})(1<p\le \infty )$ boundedness of the maximal operators associated with a family of vector polynomials given by the form $\left\{ ({{2}^{{{k}_{1}}}}{{\mathfrak{p}}_{1}}(t),...,{{2}^{{{k}_{d}}}}{{\mathfrak{p}}_{d}}(t)):t\in \mathbb{R} \right\}$. Furthermore, by using the lifting argument, we extend this result to a general class of vector polynomials whose coefficients are of the form constant times ${{2}^{k}}$.
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- Copyright © Canadian Mathematical Society 2012
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